68 ON THE PRIMITIVE FORMS OF CRYSTALS. 



presented by their lengths, the resultant of these 

 forces cannot possibly be one axis, but must necessa- 

 rily be the same as two rectangular axes, which 

 they are known to possess. 



The only exception to the generality of this ob- 

 servation, is in the case of the Right Prism with 

 a square base, which, in reference to the general 

 hypothesis, ought to have had only one axis of 

 polarisation. We do not pretend to explain this 

 very singular exception, but it is worthy of remark, 

 that Idocrase, Titanite and Uranite, to which Haiiy 

 has assigned this as the primitive form, have not 

 two axes, and therefore that it is within the limits 

 of probability that all the crystals which are ranked 

 under this form may have another primitive nu- 

 cleus. 



In the Third Class of Primitive Forms, 

 the general principle has a very remarkable appli- 

 cation. All the crystals belonging to this class, 

 have neither double refraction nor polarisation ; and 

 I have demonstrated, that if any crystal possesses 

 three equal and rectangular axes, either all posi- 

 tive or all negative, the forces which emanate from 

 them will be in perfect equilibrium in every part 

 of the crystal, and consequently there can be nei- 

 ther double refraction nor polarisation. Now, it 

 is very singular, that the cube, the regular octo- 

 hedron, and the rhomboidal dodecahedron, which 

 compose this class, are the only solids in which nei- 

 ther more nor less than three such axes can be 



